The VISCACHA survey – VI. Dimensional study of the structure of 82 star clusters in the Magellanic Clouds

We present a study of the internal structure of 82 star clusters located at the outer regions of the Large Magellanic Cloud and the Small Magellanic Cloud using data of the VISCACHA Survey. Through the construction of the minimum spanning tree, which analyzes the relative position of stars within a given cluster, it was possible to characterize the internal structure and explore the fractal or subclustered distribution for each cluster. We computed the parameters $\overline{m}$ (which is the average length of the connected segments normalized by the area), $\overline{s}$ (which is the mean points separation in units of cluster radius), and Q (the ratio of these components). These parameters are useful to distinguish between radial, homogeneous, and substructured distributions of stars. The dependence of these parameters with the different characteristics of the clusters, such as their ages and spatial distribution, was also studied. We found that most of the studied clusters present a homogeneous stellar distribution or a distribution with a radial concentration. Our results are consistent with the models, suggesting that more dynamically evolved clusters seem to have larger Q values, confirming previous results from numerical simulations. There also seems to be a correlation between the internal structure of the clusters and their galactocentric distances, in the sense that for both galaxies, the more distant clusters have larger Q values. We also paid particular attention to the effects of contamination by non-member field stars and its consequences finding that field star decontamination is crucial for these kinds of studies.